1. Field of the Invention
This invention relates to an apparatus for processing articles of diverse shapes by numerical control, and particularly to the correction of delay of a positioning mechanism thereof.
2. Description of the Prior Art
Generally, articles of non-circular cross sectional shape are processed by a milling machine or the like, but these machine tools are considerably inferior to the lathe in view of processing efficiency. On the other hand, the lathe processing, which is a processing method for cutting article by a cutting tool secured to a tool rest, is high in processing efficiency but articles obtained therefrom are limited to those having a circular cross section.
Therefore, there is a demand that articles having a sectional shape close to a relatively circular shape as shown in FIG. 1, for example, such as cams, swage processing rolls and the like are processed efficiently.
To this end, it is necessary to reciprocate a cutting tool 2 in an X direction in synchronism with rotation with a spindle 1 of the lathe, as shown in FIGS. 2 and 3, which are in the form of a conceptual view. That is, a contour of the articles as an object assumes a closed curve at a certain feed position Z as shown in FIG. 1(b). If the closed curve is represented by r=f (.theta.) using polar coordinates (r, .theta.), it is necessary to give the valve of r as a function of the rotational angle .theta. of the spindle 1 to control the nose position X of the tool 2 so as to satisfy with said value.
Actually, the command value for positioning is used by converting it to X=f(.theta.)+A or X=B-f(.theta.) by the designation of the amount of shift A, B of the origin of the positioning system and the positive and negative directions.
To control positioning the tool as described above, a servo system which input is a contour model by a hydraulic servo mechanism has been principally used. However, in this hydraulic contour mechanism, the contour model rotated in synchronism with the spindle is made to be a mechanical input of the hydraulic servo mechanism, and therefore, a contour model had to be fabricated for every shape of article. One proposal has been realized in which a cam mechanism is used to synchronize the spindle with the position of the tool rest. However, this proposal was not suitable for diversification of products likewise the case which uses the contour model.
To freely change the shape of article in order to cope with diversification of article, if the positioning control of the tool rest in the X direction is carried out by numerical control, the change of shape can be performed merely by changing a program.
Recently, some examples wherein the lathe is subjected to the numerical control have been proposed. However, these have drawbacks in that the rotational speed of the spindle is very slow, and the processing efficiency is extremely low despite the fact that the lathe is especially used.
In this numerical control (NC), the rotational angle .theta. of the spindle is detected by an angle detector such as an encoder, and the value f (.theta.) of r stored in a memory of a control device is put out to the value of the detected .theta. thereby obtaining the command value for positioning the tool.
One example of this construction is shown in FIG. 4. An encoder is mounted on a rotational shaft 1 of the spindle, and N pulses are released per revolution of the encoder. On the other hand, the following data are successively stored in N memories to repeatedly successively call memories every time the pulse is received from the encoder: ##EQU1## where n=1 to N The output enters a positioning servo mechanism in an X direction of a tool rest 3 such as an electric-hydrualic servo mechanism through a D/A converter. It is of course noted that when a computer having a capacity of high speed calculation is used, a program for calculating f (.theta.) with respect to .theta. can be employed instead of storing f(.theta.) into the memory.
The positioning servo mechanism in the X direction of the tool rest 3 requires power and high-speed responsiveness overcoming the cutting resistance. For that purpose, the electric-hydraulic servo mechanism is suitably used, but an excellent servo actuator such as a high output servo motor can be used, if available. Reference numerals 4 and 5 denote a servo valve and a servo cylinder, respectively, which constitute an electric-hydraulic servo mechanism. A reference numeral 6 denotes a connecting rod.
In such a positioning servo system, the transmission characteristic between input and output, that is, between the command value and actual position, is given by EQU Y(s)=T(s)R(s) (1)
where R (s) is input, Y (s) is output and T (s) is transmission function, and ##EQU2## (where K, a.sub.1 -a.sub.n are constant, generally, K=1)
FIG. 5 shows one example of the transmission characteristic of the electric-hydraulic servo system.
As can be seen from the equation (2) and FIG. 5, in the positioning servo system, generally, if the frequency of the input increases, delay in phase and reduction in amplitude occur.
Therefore, according to a conventional method wherein the value of f (.theta.) is merely made to be the input of the servo system with respect to the rotational angle .theta. of the spindle, where the number of revolutions of the spindle is high and f(.theta.) includes a high harmonic component with respect to .theta., it is not possible to form an exact contour due to the aforementioned delay in phase and reduction in amplitude, example of which is shown in FIGS. 6(a) and (b). The input valve (target contour) is indicated by the dotted lines and the output value is indicated by the solid lines. This is the main reason why the spindle can be rotated only at a low speed.